Nuclear weighted composition operators on weighted Banach spaces of analytic functions
Authors:
José Bonet, M. Carmen Gómez-Collado, Enrique Jordá and David Jornet
Journal:
Proc. Amer. Math. Soc. 149 (2021), 311-321
MSC (2010):
Primary 47B10, 47B33
DOI:
https://doi.org/10.1090/proc/15223
Published electronically:
September 18, 2020
MathSciNet review:
4172607
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We characterize nuclear weighted composition operators $W_{\psi ,\varphi }f=\psi (f\circ \varphi )$ on weighted Banach spaces of analytic functions with sup-norms. Consequences about nuclear composition operators on Bloch type spaces are presented. They extend previous work by Fares and Lefèvre on nuclear composition operators on Bloch spaces. Examples of nuclear as well as compact and non-nuclear weighted composition operators are given.
- Klaus D. Bierstedt, José Bonet, and Antonio Galbis, Weighted spaces of holomorphic functions on balanced domains, Michigan Math. J. 40 (1993), no. 2, 271–297. MR 1226832, DOI https://doi.org/10.1307/mmj/1029004753
- Klaus D. Bierstedt, José Bonet, and Jari Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (1998), no. 2, 137–168. MR 1488148
- José Bonet, Paweł Domański, and Mikael Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull. 42 (1999), no. 2, 139–148. MR 1692002, DOI https://doi.org/10.4153/CMB-1999-016-x
- J. Bonet, P. Domański, M. Lindström, and J. Taskinen, Composition operators between weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 64 (1998), no. 1, 101–118. MR 1490150
- M. D. Contreras and A. G. Hernandez-Diaz, Weighted composition operators in weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 69 (2000), no. 1, 41–60. MR 1767392
- John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
- Carl C. Cowen and Barbara D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. MR 1397026
- Joe Diestel, Hans Jarchow, and Andrew Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR 1342297
- Paweł Domański and Mikael Lindström, Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions, Ann. Polon. Math. 79 (2002), no. 3, 233–264. MR 1957801, DOI https://doi.org/10.4064/ap79-3-3
- Tonie Fares and Pascal Lefèvre, Nuclear composition operators on Bloch spaces, Proc. Amer. Math. Soc. 148 (2020), no. 6, 2487–2496. MR 4080891, DOI https://doi.org/10.1090/proc/14915
- Wolfgang Lusky, On the structure of $Hv_0(D)$ and $hv_0(D)$, Math. Nachr. 159 (1992), 279–289. MR 1237115, DOI https://doi.org/10.1002/mana.19921590119
- Wolfgang Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. (2) 51 (1995), no. 2, 309–320. MR 1325574, DOI https://doi.org/10.4064/sm175-1-2
- Wolfgang Lusky, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Studia Math. 175 (2006), no. 1, 19–45. MR 2261698, DOI https://doi.org/10.4064/sm175-1-2
- Alfonso Montes-Rodríguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. (2) 61 (2000), no. 3, 872–884. MR 1766111, DOI https://doi.org/10.1112/S0024610700008875
- Albrecht Pietsch, Nuclear locally convex spaces, Springer-Verlag, New York-Heidelberg, 1972. Translated from the second German edition by William H. Ruckle; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66. MR 0350360
- Joel H. Shapiro, Composition operators and classical function theory, Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993. MR 1237406
- J. H. Shapiro and P. D. Taylor, Compact, nuclear, and Hilbert-Schmidt composition operators on $H^{2}$, Indiana Univ. Math. J. 23 (1973/74), 471–496. MR 326472, DOI https://doi.org/10.1512/iumj.1973.23.23041
- A. L. Shields and D. L. Williams, Bonded projections, duality, and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), 287–302. MR 283559, DOI https://doi.org/10.1090/S0002-9947-1971-0283559-3
- Allen L. Shields and David L. Williams, Bounded projections, duality, and multipliers in spaces of harmonic functions, J. Reine Angew. Math. 299(300) (1978), 256–279. MR 487415
- Jari Taskinen, Compact composition operators on general weighted spaces, Houston J. Math. 27 (2001), no. 1, 203–218. MR 1843919
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47B10, 47B33
Retrieve articles in all journals with MSC (2010): 47B10, 47B33
Additional Information
José Bonet
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
ORCID:
0000-0002-9096-6380
Email:
jbonet@mat.upv.es
M. Carmen Gómez-Collado
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
ORCID:
0000-0003-0604-1009
Email:
mcgomez@mat.upv.es
Enrique Jordá
Affiliation:
EPS Alcoy, Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Plaza Ferrándiz y Carbonell s/n, E-03801 Alcoy, Spain
ORCID:
0000-0003-2980-1699
Email:
ejorda@mat.upv.es
David Jornet
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Camino de Vera, s/n, E-46071 Valencia, Spain
MR Author ID:
693618
ORCID:
0000-0002-3531-6203
Email:
djornet@mat.upv.es
Received by editor(s):
April 21, 2020
Received by editor(s) in revised form:
June 4, 2020
Published electronically:
September 18, 2020
Additional Notes:
The research of the authors was partially supported by the project MTM2016-76647-P. The research of the first author was partially supported by the project GV Prometeo 2017/102.
Communicated by:
Javad Mashreghi
Article copyright:
© Copyright 2020
American Mathematical Society